Trigonometric depth gauge for biopsy needle

ABSTRACT

Apparatus for determining a proper insertion depth of a biopsy needle to be inserted at a selected point on the body of a patient so that a sampling end of the needle just reaches to a designated target area within the body, comprises at least one straight calibrated pointing device, having a pivot point at one end thereof, and aligned to point through the selected point in a straight line passing through the designated target region, an image of the pointing device being formed on each of first and second image planes by utilizing radiation from respective first and second radiation source positions, along with images corresponding to the selected point and the target area. Needles are provided for casting an image on one at least one of the image planes, the needles being pivotably mounted at a further pivot point different from the pivot point of the pointing device and being constrained for movement in plane defined by the pivot point, the further pivot point and by the pointing device.

The present invention relates to a system, apparatus, and method foraccurate positioning of a surgical tool, such as a biopsy needle, withrespect to a deep seated target inside a patient and, more specifically,a positioning device that takes as its input a needle entry point and atarget point selected on the screen of a fluoroscope for automaticallypositioning a needle guide and indicating the depth to the target point.

The subject matter of the following copending patent applications beingfiled on even date herewith is closely related to the subject matter ofthe present application and is incorporated herein by reference to theextent it is not incompatible with the present disclosure APPARATUS ANDMETHOD FOR POSITIONING A BIOPSY NEEDLE Ser. No. 08/722,725, APPARATUSAND METHOD FOR AUTOMATICALLY POSITIONING A BIOPSY NEEDLE Ser. No.08/722,707, and APPARATUS AND METHOD FOR DETERMINING THE CORRECTINSERTION DEPTH FOR A BIOPSY NEEDLE Ser. No. 08/722,708. All are filedin the names of Navab and Geiger, the present inventors, and all areassigned to Siemens Corporate Research, Inc., as is the presentapplication.

Needle biopsy is one of the most frequent surgical interventions.Typically, a fine needle is used to remove tissue portions from a lesioninside the body. If the lesion is very small and is deep-seated withinthe body or is not palpable, the surgeon needs guidance in order to makesure that the tip of the needle reaches the desired location.

Currently used image based guidance methods include the following.Ultrasound (US), X-ray fluoroscopy, CT fluoroscopy, and CT/MRI incombination with real time registration tools. The first three methodsprovide real time intra-operative images of the patient and enable thesurgeon to see the needle as it approaches the target.

Ultrasound is relatively inexpensive and is a readily available imagemodality. However, its usage for guidance is limited to lesions that areclose to the skin and that show a well defined signal.

The X-ray fluoroscope is a widely available, low cost two-dimensional(2D) imaging equipment. Since it shows a two-dimensional projection, two(generally orthogonal) views are necessary in order to determine thebiopsy needle position. This can be done by turning the arm of a simplefluoroscope, such as a C-arm fluoroscope, an example of which is shownin FIG. 1, or by using a fluoroscope such as that illustrated in FIG. 2that provides two simultaneous orthogonal views. Since the needle has tobe manipulated in the image field, one cannot avoid a X-ray exposure ofthe physician when using such techniques. As is well-known, unnecessaryexposure of health workers to X-ray radiation is believed to behazardous to health and it is desirable that it should be avoided to theextent possible.

CT-Fluoroscopy permits real-time display of CT images. The physiciancontrols X-ray exposure during continuous tube rotation. The exactposition of the needle can be traced by moving the table. In the casefor CT-Fluoroscopy also, the surgeon is exposed to X-rays.

CT/MRI in combination with real time registration tools is based onpre-operative 3-D data acquisition (CT or MRI). The lesion is outlinedin the resulting dataset. During the actual biopsy, the position andorientation of the patient and the needle have to be known precisely andaligned with the pre-operative data.

Therefore two registrations have to be used for guiding the needle: thepre-operative data showing the lesion has to be registered with thepatient. This can be done by attaching invariant markers to the patient(stereo-tactic frames) before data acquisition or by matching invariantpatient features, such as the skull or bones.

The needle has to be registered with the patient. One possibility is toattach optical markers to the needle which can be tracked by a system ofcameras or by X-ray fluoroscopy, or to use mechanical devices likepassive robot arms that register the position of the needle at anymoment. This technique requires highly specialized and costly 3-Dimaging facilities that are typically only available at a few researchsites. Despite the image guidance, a successful biopsy procedure stilldepends on the manual skills and judgement of the surgeon who ismanipulating the needle.

There is a need herein recognized for an alignment device that isadjustable to the right direction and that indicates the distance to adeep-seated target. Among the benefits that result from such a deviceare acceleration of the procedure, increase of the safety of theprocedure, and reduction of radiation exposure for both the patient andfor the surgeon.

In accordance with the objects of the present invention, an X-ray imageguided system provides assistance in the execution of needle biopsy. Itcan also be used for minimal access surgical procedures, known as“keyhole surgery”. One of the objects of the present system, which issimple and readily implemented, is to help surgeons overcomedifficulties associated with positioning the biopsy needle or performingminimally invasive surgery in three dimensions while utilizingtwo-dimensional images for guidance in the procedure.

Another object of the present invention is to practically eliminate orreduce to a minimum the need for a surgeon's reliance on a radiologistto open an access track pre-operatively in the radiology suite.

Furthermore, another object of the invention is to practically eliminatethe need for accurate geometrical calibration. The present invention isbelieved to provide a first opportunity in which quantitative imagingguidance is made possible without a dedicated geometrical calibrationprocedure.

The invention permits the accurate positioning of a surgical tool, suchas biopsy needle, with respect to a deep seated target inside a patient.It is the practical application of an algorithm in accordance with theinvention which makes the accurate positioning possible.

In accordance with the invention, the depth of a deep-seated targetwithin a patient's body is readily computed from one single radiographicimage. Based on geometrical reasoning involving a mechanical device,simple in conception, in accordance with the invention, biopsy needlesmay be considered in the context of the invention as an adjunct totraditional medical imaging systems such as C-arm equipment andfluoroscopes.

Generally, a preferred position for a biopsy needle from the surgicalpoint of view is a position above the patient from which it goes throughthe organ of interest. In addition, the surgeon needs to know the depthof the target in order to correctly insert the needle.

In accordance with an aspect of the invention, apparatus for determiningthe required insertion depth for a biopsy needle priorly aligned forproper insertion into the body of a patient at a selected point on asurface of the body, so as to enter in a straight line passing through adesignated target region within the body by the use of first and secondimage planes, such that at the proper depth, an end of the needle justreaches the target area, comprises: a base portion including a circleportion having a center point; a planar semicircular portion mountedonto the base portion such that the diameter of the semicircular portionis concentric with the center point and rotatable thereabout, thesemicircle portion being further rotatable about a straight line throughthe diameter; a straight pointing device having one end thereofpivotably affixed to the center point and being constrained for movementwithin a plane defined by the planar semicircular portion; and at leastone straight pointing needle having one end thereof pivotably affixed atone end of the diameter of the semicircular portion and beingconstrained for movement within a plane defined by the planarsemicircular portion.

In accordance with another aspect of the invention, apparatus fordetermining the required insertion depth for a biopsy needle includesapparatus for measuring an angle Θ of the plane defined by thesemicircular portion relative to the base portion, an angle φ of thepointing device relative to the base portion, and an angle φ₁ defined bythe at least one pointing needle relative to the base portion.

In accordance with another aspect of the invention, apparatus fordetermining the required insertion depth for a biopsy needle includes afurther pointing needle having one end thereof pivotably affixed at theother end of the diameter of the semicircular portion and beingconstrained for movement within the plane defined by the planarsemicircular portion.

In accordance with an aspect of the invention, at least one of thepointing needles is made of relatively radiation-transparent material.

In accordance with another aspect of the invention, at least one of thepointing needles is made of relatively radiation-transparent materialand includes imbedded therein radiation-opaque markers.

In accordance with another aspect of the invention, the depth isobtained by solving the equation

${A\; C} = {{\sin\left( \phi_{1} \right)} \times \frac{A\; B}{\sin\left( {\phi_{1} - \phi} \right)}}$

In accordance with another aspect of the invention, apparatus fordetermining the required insertion depth for a biopsy needle priorlyaligned for proper insertion into the body of a patient at a selectedpoint on a surface of the body, so as to enter in a straight linepassing through a designated target region within the body by the use offirst and second image planes, such that at the proper depth, an end ofthe needle just reaches the target area, comprises: a base including afirst planar measuring portion having a center point; a second planarmeasuring portion mounted onto the base portion such that a center pointof the second measuring portion is concentric with the center point ofthe first planar measuring portion so that the second planar measuringportion is rotatable about the center point, the second planar measuringportion being further rotatable about a straight line through itscenter; and an essentially straight pointing device having one endthereof pivotably affixed to the center point and being constrained formovement within a plane defined by the planar semicircular portion; andat least one essentially straight pointing needle having one end thereofpivotably affixed at one end of the straight line of the semicircularportion and being constrained for movement within a plane defined by theplanar semicircular portion.

In accordance with another aspect of the invention, apparatus fordetermining a proper insertion depth of a biopsy needle to be insertedat a selected point on the body of a patient so that a sampling end ofthe needle just reaches to a designated target area within the body,comprises: at least one straight calibrated pointing device, having apivot point at one end thereof, and aligned to point through theselected point in a straight line passing through the designated targetregion, an image of the pointing device being formed on each of firstand second image planes by utilizing radiation from respective first andsecond radiation source positions, along with images corresponding tothe selected point and the target area; and needle apparatus for castingan image on one at least one of the image planes, the needle apparatusbeing pivotably mounted at a further pivot point different from thepivot point of the pointing device and being constrained for movement inplane defined by the pivot point, the further pivot point and by thepointing device.

In accordance with another aspect of the invention, apparatus fordetermining a proper insertion depth of a biopsy needle to be insertedat a selected point on the body of a patient so that a sampling end ofthe needle just reaches to a designated target area within the body,comprises at least one straight calibrated pointing device pivoted atone end thereof at a pivot point; positioning apparatus forautomatically positioning or aligning the at least one straightcalibrated pointing device as a guide for a biopsy needle for properinsertion into the body of a patient from a selected point on a surfaceof the body, so as to enter in a straight line passing through adesignated target region within the body, in conjunction with an imagingsystem utilizing radiation from a first source position for deriving afirst radiographic image on a first image plane of a portion of the bodyincluding a first image of the selected point and a first image of thetarget region, the first source position, the first image of theselected point, and the first image of the target region defining afirst viewing plane π, the imaging system utilizing radiation from asecond source position for deriving a second radiographic image on asecond image plane of the portion of the body, including a second imageof the selected point and a second image of the target region, thesecond source position, the second image of the selected point, and thesecond image of the target region defining a second viewing plane π′,the positioning apparatus comprising: measurement apparatus fordetermining an angle Θ₁ for a selected first auxiliary plane and anangle Θ₂ for a selected second auxiliary plane with respect to aselected set of coordinates and for storing the angles, the second planeangle being different from the first plane angle such that the first andsecond auxiliary planes form an intersection line; apparatus forconstraining the calibrated pointing device for moving rotatably aboutthe selected point and within the first auxiliary plane to a first angleof inclination φ₁ relative to sa set of coordinates and for controllingthe calibrated pointing device such that a projection or extension of animage of the calibrated pointing device on the first image plane passesthrough the first image of the target region and for storing the angleφ₁, the alignment and control apparatus further controlling thecalibrated pointing device for moving rotatably about the selected pointand within the second auxiliary plane to a second angle of inclinationφ₂ relative to the set of coordinates such that a projection orextension of an image of the calibrated pointing device on the secondimage plane passes through the second image of the target region and forstoring the angle φ₂, whereby the first viewing plane π is uniquelydefined by the angles Θ₁, Θ₂, φ₁, and φ₂ relative to the set ofcoordinates; apparatus for determining orientation angles α and Θ₃ ofthe viewing plane π from stored values of the angles Θ₁, Θ₂, φ₁, and φ₂,and storing the angles α and Θ₃; and apparatus for moving the calibratedpointing device rotatably about the selected point and within the firstviewing plane π, as defined by the angles α and Θ₃, to a third angle ofinclination φ₃ relative to the set of coordinates such that a projectionor extension of an image of the calibrated pointing device on the secondimage plane passes through the further image of the target region,whereby the pointer points directly through the selected point towardthe target region, such that that respective images of pointing deviceare formed on the first and second image planes, along with imagescorresponding to the selected point and the target area; and needleapparatus for casting an image on one at least one of the image planes,the needle apparatus being pivotably mounted at a further pivot pointdifferent from the pivot point of the pointing device and beingconstrained for movement n plane defined by the pivot point, the furtherpivot point and by the pointing device.

In accordance with another aspect of the invention, a method fordetermining the required insertion depth for a biopsy needle so as tojust reach a selected target area within a body, wherein a properdirection for insertion of the biopsy needle has been priorly determinedfrom a radiographic image on a viewing plane such that an extension ofthe direction of the biopsy needle from a selected insertion point intothe body in a straight line leads through a selected target area,comprises the steps of: defining a plane containing the biopsy needle;adjusting a pointing needle, pivoted at one end and constrained to movewithin the plane, until a prologation of the line of an image of thepointing needle on the plane intersects the selected target area; andcalculating the required insertion depth from knowledge of a base linelength AC joining the pivot point and the selected insertion point andrespective angles, φ and φ₁, of the biopsy needle and the pointingneedle.

In accordance with another aspect of the invention, the requiredinsertion depth for a biopsy needle in accordance with claim 17 whereinthe required insertion depth is given by

${A\; C} = {{\sin\left( \phi_{1} \right)} \times \frac{A\; B}{\sin\left( {\phi_{1} - \phi} \right)}}$

In accordance with another aspect of the invention, apparatus fordetermining the required insertion depth for a biopsy needle priorlyaligned for proper insertion into the body of a patient at a selectedpoint on a surface of the body, so as to enter in a straight linepassing through a designated target region within the body by the use offirst and second image planes, such that at the proper depth, an end ofthe needle just reaches the target area, the apparatus comprising: abase portion including a circle portion having a center point; a planarsemicircular portion mounted onto the base portion such that thediameter of the semicircular portion is concentric with the center pointand rotatable thereabout, the semicircle portion being further rotatableabout a straight line through the diameter; a straight pointing devicehaving one end thereof pivotably affixed to the center point and beingconstrained for movement within a plane defined by the planarsemicircular portion; and first and second essentially straight pointingneedles, each having one end thereof pivotably affixed at a respectiveend of the diameter of the semicircular portion and being constrainedfor movement within a plane defined by the planar semicircular portion.

In accordance with another aspect of the invention, apparatus fordetermining a proper insertion depth of a biopsy needle to be insertedat a selected point on the body of a patient so that a sampling end ofthe needle just reaches to a designated target area within the body,comprises at least one straight calibrated pointing device, having apivot point at one end thereof, and aligned to point through theselected point in a straight line passing through the designated targetregion, an image of the pointing device being formed on each of firstand second image planes by utilizing radiation from respective first andsecond radiation source positions, along with images corresponding tothe selected point and the target area. Needles are provided for castingan image on one at least one of the image planes, the needles beingpivotably mounted at a further pivot point different from the pivotpoint of the pointing device and being constrained for movement in planedefined by the pivot point, the further pivot point and by the pointingdevice.

The invention will be further understood from the detailed descriptionof the prefered embodiments, in conjunction with the drawing in which:

FIG. 1 shows a known type of C-arm fluoroscope, such as may be utilizedin conjunction with the present invention;

FIG. 2 shows a known type of fluoroscope with two simultaneousorthogonal views, such as may be utilized in conjunction with thepresent invention;

FIG. 3 shows a diagrammatic configuration of imaging radiation sources,image screens and a target area, helpful in understanding the invention;

FIGS. 4, 5, and 6 show various steps of a method utilizable inconjunction with the invention;

FIGS. 7 and 8 show diagramatically apparatus and principles helpful toan understanding of the objects of the invention;

FIGS. 9, 10, and 11 show various steps of a method utilizable inconjunction with the invention;

FIGS. 12, 13, and 14 show diagramatic representations of apparatusutilizable in conjunction with the invention;

FIG. 15 shows a system diagram in accordance with the invention;

FIG. 16 a diagramatic representation of apparatus in accordance with theinvention;

FIGS. 17, 18, and 19 show flow charts helpful to gaining anunderstanding of the invention;

FIG. 20 shows components of an automatic system and theirinterrelationship of a method utilizable in conjunction with theinvention.

Apparatus and diagram drawings are not necessarily to scale.

FIG. 3 shows the geometry desirable for the surgeon. Preferably, thebiopsy needle should be positioned such that its straight linecontinuation, or virtual extension, passes through a deep-seated targetT inside the patient. During the manual procedure, the surgeon keeps thebottom end F of the needle on or near the patient's body and changes itsdirection until the virtual extension of the needle passes through theradiographic image t of the target T. The correct needle direction hasto be verified on two radiographs that are taken from different angles.

In accordance with the present invention an apparatus has a geometricalconfiguration embodying a reasoned interpretation of what the surgeonseeks to do intuitively during a manual adjustment procedure. Clearly,the surgeon does not compute the exact or relative position andorientation of the C-arm and the image plane during a more or lessrefined “hit or miss” procedure. Rather, the surgeon proceeds by simplereasoning directly from radiographic images to the moving needle.

The subject matter of the above-mentioned copending patent applicationsentitled APPARATUS AND METHOD FOR POSITIONING A BIOPSY NEEDLE, APPARATUSAND METHOD FOR AUTOMATICALLY POSITIONING A BIOPSY NEEDLE, and APPARATUSAND METHOD FOR DETERMINING THE CORRECT INSERTION DEPTH FOR A BIOPSYNEEDLE is an adjunct to and is helpful to an understanding of thepresent invention and accordingly is herein included.

Referring again to FIG. 3, the imaging system is modelled approximatelyas a “pinhole camera” model. The optical center, S, represents thelocation of the X-ray source and the position and orientation of animage intensifier defines the image plane, I. The deep-seated targetinside patient's body is indicated by T, with t being its radiographicimage.

F is a fixed point from where the surgeon wishes to insert the biopsyneedle. f is its radiographic image. The viewing plane π is defined bythe optical center, S, the target on the image, t, and the fixed point,F, and its radiographic image, f.

All the entities and reference letters relating to a second position ofthe X-ray and therefore to a second radiographic image are noted byprime, such as S′, π′, and so on.

Initially, it is recognized that the three-dimensional position ofviewing plane π, while obtainable in accordance with the presentdisclosure as will be shown, is not known in a facile manner to theuser.

Generally, images of all lines lying on the plane π which do not passthrough the optical center S, are collinear to the line ft on theradiographic image I. Since the depth of the target T, or ∥FT∥, isunknown, the maximum information that can be obtained on the positionand orientation of the biopsy needle from a sequence of images takenfrom a single viewpoint is the three dimensional position of the planeπ. Accordingly, a first part of the algorithm in accordance with thepresent disclosure can be established, in Step I, as follows.

Any plane π₁ passing through the fixed point F, other than the plane πitself, intersects the plane π in one line. This line clearly containsthe point F and therefore its image must pass through the image f of thefixed point F on the image on image plane I. The first two steps of thealgorithm can now be defined, resulting in a method of accuratelyobtaining the three dimensional coordinates of the viewing plane π. Ametallic, or other radiation-opaque, bar is rotated around the fixedpoint F in an arbitrary plane π₁ passing through the fixed point F. SeeFIG. 4, which illustrates the step of finding a three-dimensional linelying on the viewing plane π. The shortest distance of the projectionline of the three-dimensional line from the target t on the image iscalled h₁.

This h₁ distance decreases as the angle between them closes, andprojection line approaches line L₁, representing the intersection of theplanes π and π₁, and vanishes at the intersection of these two planes.This provides a simple way to control the metallic bar under automaticimages guidance and move it until it lies on the plane π.

In a further step, Step II, a metallic (X-ray opaque) bar is rotatedaround the fixed point F in a second plane π₂ passing through the fixedpoint F, and different from π₁ used in the Step I, see FIG. 5, whichillustrates the procedure for finding a second three-dimensional line onthe viewing plane π. Preferably, the plane passing through F andorthogonal to π₁ is selected as π₂. The distance of its projection linefrom the target t on the image, is called h₂. This distance decreases asthe projection line of π₂ approaches line L₂, representing theintersection of the planes π and π₂ and this distance, h₂ vanishes atthe intersection line of these two planes.

This provides a way to control a second metallic bar under automaticimages guidance and move it until it also lies on the plane π. Now twodistinct lines, L₁ and L₂, having a non-zero angle of intersectiontherebetween, are identified on the plane π. These lines uniquely definethe plane π in three dimensional space. This is the maximum informationthat can be had from a single viewpoint with no calibration data.

A next step, Step III, is the use of a second viewpoint. Theradiographic image from a second viewpoint can be obtain either bymoving the C-arm of the machine arbitrarily; the larger is the angle ofrotation the more accurate is the resulting position and orientation ofthe needle.

The plane defined by the optical center, the X-ray source S′ of the newconfiguration of the imaging system, the target T and the fixed point Fis designated as π′, analogous to plane π in the previous determination.See FIG. 6 which shows the procedure for finding the right orientationfor the biopsy needle.

A metallic bar is rotated around the fixed point F in the plane πobtained in step II. The distance of its projection line, 1′, from thetarget t′ on the image taken from the new viewpoint, is called h′. Thisdistance decreases as one gets closer to the line L′, representing theintersection of the planes π and π′ and this distance vanishes at theintersection of these two planes.

This provides a way to control the metallic bar manually orautomatically using image guidance and move it until the line FT isfound. FT is the line of intersection of the two flat planes π and π′and it therefore represents a vector direction in space passing throughthe proposed fixed insertion point F and, when produced, through thetarget T. Now, the surgeon can be guided to the correct positioning ofthe biopsy needle. The next step in accordance with the invention, is tolet the surgeon know how deep the target T is inside the patient. Firsta method disclosed in the copending application entitled APPARATUS ANDMETHOD FOR DETERMINING THE CORRECT INSERTION DEPTH FOR A BIOPSY NEEDLEwill be described.

The cross ratio is a fundamental invariant of perspective projection.See, for example, O. D. Faugeras, Three-Dimensional Computer Vision: AGeometric Viewpoint; MIT Press, Cambridge, Mass.; 1993. This invariantcan be used here to accurately compute FT, the depth of the targetinside patient's body.

Referring to FIG. 7, consider the four points A, B, C, and D, on a linein space. The cross ratio of these four points can be defined as

$\frac{A\; B \times C\; D}{A\; C \times B\; D}.$The perspective projection of these four points on any plane and withrespect to any projection center, for example {a, b, c, d} and {e, f, g,h} in FIG. 7 results in the same cross ratio between the projectedpoints:

$\frac{A\; B \times C\; D}{A\; C \times B\; D} = {\frac{a\; b \times c\; d}{a\; c\; \times b\; d} = \frac{e\; f \times g\; h}{e\; g \times f\; h}}$

For the case of two markers, M₁ and M₂, on the metallic bar used in stepIII, such that ∥M₁F∥ and ∥M₂F∥ are accurately known, and m₁′ and m₂′,their radiographic images, are easily and accurately detectable, seeFIG. 8. The assumptions made are reasonable and readily realized inpractice. The cross ratio computed for the image points [m′1, m′2, f′,t′] is the same as the cross ratio of the four points [M₁, M₂, F, T] inthe three dimensional space. The positions of all these points otherthan T are known. FT is then computed from the following equation:

${{F\; T}} = {{\frac{\lambda \times {{M_{1}F}} \times {{M_{2}F}}}{{{M_{1}M_{2}}} - {\lambda \times {{M_{1}F}}}}\mspace{31mu}{where}\mspace{25mu}\lambda} = \frac{\frac{{f^{\prime}t^{\prime}}}{{m_{2}^{\prime}t^{\prime}}}}{\frac{{m_{1}^{\prime}f^{\prime}}}{{m_{1}^{\prime}m_{2}^{\prime}}}}}$

The positioning in accordance with the present disclosure is designedbased on the algorithm disclosed above. FIGS. 12, 13, 14, and 16 show adesign configuration. A part of the apparatus is a semi-circle that canrotate at least from 0 to 180 degrees around the center of a circularbase. This rotation angle is designated by α in FIG. 12. Thissemi-circle has a second degree of freedom: it can also turn around itsown baseline from 0 to 180 degrees. This rotation angle is designated byΘ in FIG. 12. A metallic bar can rotate on the plane defined by thissemi-circle from 0 to 180 degrees. This rotation angle is noted by φ inFIG. 12. This provides all that is required. All rotations can be doneeither by hand, by command, or automatically. The parallel or serialconnection between a computer, such as a personal computer (PC), and apositioning device can guide the system based on the minimization of h₁,h₂ and h′ on the radiographic images. Further details about theinteractive and automatic process are provided in appendix-A andappendix-B.

FIGS. 9, 10, and 11 provide bridging information to facilitate anunderstanding of the relationship between the foregoing algorithm andthe design herein described. These figures include some of theconstructions shown in previous figures and are helpful to bridging thesteps between the geometric principles forming a basis for the presentinvention and the practical apparatus and method herein disclosed.

FIG. 9 shows the procedure utilized in finding one three dimensionalline lying on the viewing plane π. This comprises positioning thesemi-circle at an arbitrary position to define a plane π₁ and thenmoving the metallic bar mounted on the semi-circle to a position whereits image passes through f and t on the image. This process can be doneautomatically. The metallic bar is moved to minimize the distance h₁ onthe image. This process is not time-consuming and is readily carried outin real time.

FIG. 10 shows Step II, the process of finding a second three dimensionalline lying on the viewing plane π. This is similar to the previous step,but the semi circle has turned by an angle in the order 90 degreesaround its based line defining a new plane π₂.

FIG. 11 shows Steps III \& IV: Finding the right orientation of thebiopsy needle and the depth of the target T inside the patient's body.This comprises positioning the semi-circle in the plane, π′ defined bythe metallic bar in steps I and II, and then rotating the metallic baruntil its radiographic view from the new viewpoint passes through f′ andt′. The center of the circular base, F, and the target inside patient'sbody, T, lie on the both planes π and π′. Their intersection istherefore FT the correct direction of the biopsy needle. The depth ofthe target, |FT|, can then be computed using the invariance of crossratios by perspective projection; see the previous section on thegeometrical description. The whole process, steps I through IV, can bedone in real time and the surgeon can easily move the device and findthe new orientation of the biopsy needle and depth of the target at anyother contact point on the patient's body. This design lends itselfreadily to economical implementation.

The interactive system in accordance with the present invention has theadvantage of being an independent unit which can be used together withany kind of X-ray fluoroscopes or C-arm imaging system and it needs nophysical connections with the imaging system. The unit is entirely andreadily portable. Furthermore, the operating surgeon has no radiationexposure at all during the search for the correct position.

FIG. 15 shows a protocol for the interactive system as herein described,in accordance with the invention. In this case the apparatus is fixed onthe patient on top of the desired entry point defined by the surgeon.The surgeon works with the control device while looking at theradiographs and can be in the same room or in another room where theradiographic images can be observed without the surgeon's being exposedto the radiation.

These are the consecutive steps of the process.

A first plane is taken by fixing α=0 and Θ=Θ₁. See FIG. 13. Note that Θ₁is quite arbitrary. A user can choose this plane so as to maintain aclear view of the metallic bar. This can be done using the controlbuttons, π₁, +α, −α, +Θ and −Θ, as shown in FIG. 15.

The user then selects the proper angle φ by moving the metallic baruntil its radiographic image passes through the target point. This canbe done by using buttons +φ and −φ as in FIG. 15. The orientation of themetallic bar is then defined as:L ₁=[sin(φ₁)sin(θ₁),sin(φ₁)cos(θ₁),cos(φ₁)]]

See FIG. 13. Note that Θ₂ is also arbitrary. A user can choose thisplane in order to have a clear view of the metallic bar. This can bedone using the control buttons, π₂, +Θ, and −Θ, as in FIG. 15.

A user finds the right angle φ by moving the metallic bar until itsradiographic image passes through the target point. This can be done byusing buttons +φ and −φ, as in FIG. 15. The orientation of the metallicbar is then defined as:L ₂=[sin(φ₂)sin(θ₂),sin(φ₂)cos(θ₂),cos(φ₂)]

The final viewing plane (see FIG. 14) is then defined by[θ=arc sin(¦¦L ₁ ΛL ₂¦¦)] and

$\alpha = {\arccos\left( \frac{{{L_{1}\lbrack 3\rbrack}{L_{2}\lbrack 1\rbrack}} - {{L_{1}\lbrack 1\rbrack}{L_{2}\lbrack 3\rbrack}}}{\sqrt{\left( {{{L_{1}\lbrack 3\rbrack}{L_{2}\lbrack 1\rbrack}} - {{L_{1}\lbrack 1\rbrack}{L_{2}\lbrack 3\rbrack}}} \right)^{2} + \left( {{{L_{1}\lbrack 3\rbrack}{L_{2}\lbrack 2\rbrack}} - {{L_{1}\lbrack 2\rbrack}{L_{2}\lbrack 3\rbrack}}} \right)^{2}}} \right)}$where Λ is the vector product defined in R³, 3-dimensional space. Thesystem will automatically move to the right position and the user has noneed to adjust Θ and α in this case.

The user then uses the image on the second image intensifier or movesthe C-arm to a new position.

The user finds the proper angle φ by moving the metallic bar until itsradiographic images passes through the target point. This can be done byusing buttons +φ and −φ as shown in FIG. 15. This is the correctorientation of the needle to be used for the biopsy.

In order to compute the depth of the target in accordance with thepresent invention, two other auxiliary needles are placed on the baseline of the semi-circle; see FIG. 16. In order not to disturb the imageof the main needle, these needles can be made in acrylic (transparent toX-ray) with only a few metallic markers to be aligned with the deepseated target. The determination of depth is arrived at by a process oftriangulation in which a base-line forms the base of a triangle with thedirections of the other two sides of the triangle being determined byrespective angles subtended by the base and the respective side.Accordingly, the accuracty is greater where the angle between a needleand the metallic bar is greater. Hence, two alternative needles areprovided so that that needle is utilized which is on the side of theobtuse angle made by the metallic bar with the plane of the diameter ofthe semicircle.

Each of these needles can rotate in the plane defined by thissemi-circle around a fixed point other than the entry point. Inaccordance with the present embodiment, the two end points of the baseline are used as the two centers of rotation. In the final position, theplane defined by the semi-circle also includes the deep seated target.

Once the correct orientation of the needle is found, the systemactivates that one of the auxiliary needles which has the greater anglewith the main needle. The user moves this needle to align it with thetarget on the image. The system computes the depth of the target bycomputing the distance between the entry point and the intersection ofthe main needle and the active auxiliary needle. FIG. 16 shows thisconstruction in detail.

The depth to the target, AC, is given by the trigonometric formula

${A\; C} = {{\sin\left( \phi_{1} \right)} \times \frac{A\; B}{\sin\left( {\phi_{1} - \phi} \right)}}$

FIG. 17 shows a flowchart of the interactive process in accordance withthe principles of the invention.

A semi-automatic system in accordance with the invention reduces thehuman interaction to the initial fixation of the unit on the patient, adefinition, such as a manual definition, of the tumor on a computerdisplay, and the final insertion of the needle, that will remain fullyunder the control of the surgeon.

The search for the optimal needle position and the calculation of thetarget depth is done automatically. The benefits of such a system aresubstantially increased speed of operation and thus less patientdiscomfort, reduced risk of patient motion, reduced radiation for thepatient, and complete elimination of radiation for the surgeon duringthe search for the position.

The automatic system utilizes as a starting point the same basicarrangement as the manual version with additional features.

Three effectors are included, such as drive motors, to change the needleposition. One each is utilized for Θ, one for φ, and one for therotation α, respectively. X-ray opaque markers are provided on thebiopsy needle guidance so as to be visible on the fluoroscopic imagesand to be readily detectable by an image processing unit.

A computer is linked to the fluoroscope so as to be able to capture andstore the X-ray images and to perform the necessary image processing todetect the needle markers. A computer stores and calculates needlepositions and commands the effectors so as to move the needlepositioner. Furthermore, a user interface to the computer allows thesurgeon to draw the outline of the target on the fluoroscopy image witha computer “mouse” coordinate translator or by using a graphics tablet.

Essentially, the procedure is as follows. The unit is installed on thepatient. One single image from the fluoroscope is stored and displayedon the computer screen. The surgeon outlines manually the tumor on thisimage using the mouse. During this stage of the interaction, thefluoroscope is turn off, thereby reducing radiation exposure. Thecomputer selects a first plane Θ and performs a task that is known asvisual servoing. See FIG. 18. It changes the needle position, therebyvarying φ and detects the needle markers on the fluoroscopic image. Fromthe markers, it can determine the projection of the needle, that is theaxial center-line of the needle produced or continued beyond the needle.

The closest distance of this “virtual needle” to the target in the imagecan be calculated. The position of the needle is changed until thisdistance is reduced to a minimal amount and the projection of the needlepasses through the target. The parameters Θ and φ of the needle positionare stored. This step is repeated for a different choice of Θ in orderto find a second needle position. Then the C-arm position has to bechanged, and the target must be outlined once again on a first image.From the two previous needle positions, the computer calculates thenecessary rotations α and Θ to bring the needle in the final plane.

Then the visual servoing step is repeated. The final position φ is theone that passes through the target. The needle guidance system has to beblocked in that position, either using the effectors or by actuating anadditional blocking or position locking device.

The fluoroscopy unit is switched on for two initial images that are usedfor outlining the target, and during the visual servoing steps. Thisprocedure is usually very brief. The system then uses the needle markersin order to automatically compute the depth of the target from the entrypoint. Depending on the speed of the effectors, the described system isable to find the optimal needle position and the depth of the target ina few seconds. FIG. 19 shows a flowchart of this automatic process. FIG.20 shows the connection and relationship between the differentcomponents of the automatic system.

It generally noted that apparatus parts should be X-ray transparentunless they are required to be visible in the image, such as, forexample, needles and markers.

While the invention has been described in terms of exemplaryembodiments, it will be apparent to one of skill in the art to which itpertains that various changes and modifications can be made withoutdeparting from the spirit of the invention. For example, circular scalesare defined in the traditional manner of a circular protractor forportions of apparatus defining a plane and providing angle measure.Clearly, such parts need not be circular to provide such functions.Furthermore, it is noted that the cross-product, while convenientlydefined and used in a particular manner herein, such as A,B and C,D, canutilize other dimensions in the constellation so as to obtain the depth.These are equivalent cross-product functions and can be substitute whereappropriate. Such changes and modifications and the like are intended tobe within the scope of the invention which is defined by the claimsfollowing.

1. Apparatus for determining the required insertion depth for a biopsyneedle priorly aligned for proper insertion into the body of a patientat a selected point on a surface of said body, so as to enter in astraight line passing through a designated target region within saidbody by the use of first and second image planes, such that at saidproper depth, an end of said needle just reaches said target area, saidapparatus comprising: a base portion including a circle portion having acenter point; a planar semicircular portion mounted onto said baseportion such that the diameter of said semicircular portion isconcentric with said center point and rotatable thereabout, saidsemicircle portion being further rotatable about a straight line throughsaid diameter; a straight pointing device having one end thereofpivotably affixed to said center point and being constrained formovement within a plane defined by said planar semicircular portion; andat least one straight pointing needle having one end thereof pivotablyaffixed at one end of said diameter of said semicircular portion andbeing constrained for movement within a plane defined by said planarsemicircular portion; means for measuring an angle θ of said planedefined by said semicircular portion relative to said base portion, anangle φ of said pointing device relative to said base portion, and anangle φ₁ defined by said at least one pointing needle relative to saidbase portion; and a further pointing needle having one end thereofpivotably affixed at the other end of said diameter of said semicircularportion and being constrained for movement within said plane defined bysaid planar semicircular portion.
 2. Apparatus for determining therequired insertion depth for a biopsy needle in accordance with claim 1,wherein at least one of said pointing needles is made of a substantiallyradiation-transparent material.
 3. Apparatus for determining therequired insertion depth for a biopsy needle in accordance with claim 1,wherein at least one of said pointing needles is made of a substantiallyradiation-transparent material and includes imbedded therein markersthat are relatively radiation-opaque as compared with saidradiation-transparent material.
 4. Apparatus for positioning or aligninga biopsy needle for proper insertion in accordance with claim 3 whereinsaid first and second planar measuring portions include a read-outdevice for reading out angles between said base, said first and saidsecond planar measuring portions, and said pointing device.
 5. Apparatusfor positioning or aligning a biopsy needle for proper insertion inaccordance with claim 4 wherein said read-out device is an electronicdigital device.
 6. Apparatus for positioning or aligning a biopsy needlefor proper insertion in accordance with claim 4 including a lockingdevice for holding said angles.
 7. Apparatus for determining therequired insertion depth for a biopsy needle in accordance with claim 1,including computing apparatus for determining said depth by solving theequation${A\; C} = {{\sin\left( \phi_{1} \right)} \times {\frac{A\; B}{\sin\left( {\phi_{1} - \phi} \right)}.}}$8. Apparatus for determining the required insertion depth for a biopsyneedle priorly aligned for proper insertion into the body of a patientat a selected point on a surface of said body, so as to enter in astraight line passing through a designated target region within saidbody by the use of first and second image planes, such that at saidproper depth, an end of said needle just reaches said target area, saidapparatus comprising: a base including a first planar measuring portionhaving a center point; a second planar measuring portion mounted ontosaid base portion such that a center point of said second measuringportion is concentric with said center point of said first planarmeasuring portion so that said second planar measuring portion isrotatable about said center point, said second planar measuring portionbeing further rotatable about a straight line through its center; and anessentially straight pointing device having one end thereof pivotablyaffixed to said center point and being constrained for movement within aplane defined by said planar semicircular portion; and at least oneessentially straight pointing needle having one end thereof pivotablyaffixed at one end of said straight line of said semicircular portionand being constrained for movement within a plane defined by said planarsemicircular portion; means for measuring an angle Θ of said planedefined by said second planar measuring portion relative to said baseportion, an angle φ of said pointing device relative to said baseportion, and an angle φ₁ defined by said at least one pointing needlerelative to said base portion; and a further pointing needle having oneend thereof pivotably affixed at the other end of said straight line andbeing constrained for movement within said plane defined by said secondplanar measuring portion.
 9. Apparatus for determining the requiredinsertion depth for a biopsy needle in accordance with claim 8, whereinat least one of said pointing needles is made of relativelyradiation-transparent material.
 10. Apparatus for determining therequired insertion depth for a biopsy needle in accordance with claim 8,wherein at least one of said pointing needles is made of relativelyradiation-transparent material and includes imbedded thereinradiation-opaque markers.
 11. Apparatus for determining the requiredinsertion depth for a biopsy needle in accordance with claim 8, whereinsaid depth is obtained by solving the equation${A\; C} = {{\sin\left( \phi_{1} \right)} \times {\frac{A\; B}{\sin\left( {\phi_{1} - \phi} \right)}.}}$12. Apparatus for determining the required insertion depth of a biopsyneedle to be inserted at a selected point on the body of a patient sothat a sampling end of said needle just reaches to a designated targetarea within said body, said apparatus comprising: at least one straightcalibrated pointing device, having a pivot point at one end thereof, andaligned to point through said selected point in a straight line passingthrough said designated target region, an image of said pointing devicebeing formed on each of first and second image planes by utilizingradiation from respective first and second radiation source positions,along with images corresponding to said selected point and said targetarea; and needle means for casting an image on one at least one of saidimage planes, said needle means being pivotably mounted at a furtherpivot point different from said pivot point of said pointing device andbeing constrained for movement in plane defined by said pivot point,said further pivot point and by said pointing device.
 13. Apparatus fordetermining a proper insertion depth of a biopsy needle to be insertedat a selected point on the body of a patient so that a sampling end ofsaid needle just reaches to a designated target area within said body,said apparatus comprising: at least one straight calibrated pointingdevice pivoted at one end thereof at a pivot point; positioning meansfor automatically positioning or aligning said at least one straightcalibrated pointing device as a guide for a biopsy needle for properinsertion into the body of a patient from a selected point on a surfaceof said body, so as to enter in a straight line passing through adesignated target region within said body, in conjunction with animaging system utilizing radiation from a first source position forderiving a first radiographic image on a first image plane of a portionof said body including a first image of said selected point and a firstimage of said target region, said first source position, said firstimage of said selected point, and said first image of said target regiondefining a first viewing plane π, said imaging system utilizingradiation from a second source position for deriving a secondradiographic image on a second image plane of said portion of said body,including a second image of said selected point and a second image ofsaid target region, said second source position, said second image ofsaid selected point, and said second image of said target regiondefining a second viewing plane π′, said positioning means comprising:measurement means for determining an angle Θ₁ for a selected firstauxiliary plane and an angle Θ₂ for a selected second auxiliary planewith respect to a selected set of coordinates and for storing saidangles, said second plane angle being different from said first planeangle such that said first and second auxiliary planes form anintersection line; means for constraining said calibrated pointingdevice for moving rotatably about said selected point and within saidfirst auxiliary plane to a first angle of inclination φ₁ relative to aset of coordinates and for controlling said calibrated pointing devicesuch that a projection or extension of an image of said calibratedpointing device on said first image plane passes through said firstimage of said target region and for storing said angle φ₁, saidalignment and control means further controlling said calibrated pointingdevice for moving rotatably about said selected point and within saidsecond auxiliary plane to a second angle of inclination φ₂ relative tosaid set of coordinates such that a projection or extension of an imageof said calibrated pointing device on said second image plane passesthrough said second image of said target region and for storing saidangle φ₂, whereby said first viewing plane π is uniquely defined by saidangles Θ₁, Θ₂, φ₁, and φ₂ relative to said set of coordinates; means fordetermining orientation angles α and Θ₃ of said viewing plane π fromstored values of said angles Θ₁, Θ₂, φ₁, and φ₂, and storing said anglesα and θ₃; and means for moving said calibrated pointing device rotatablyabout said selected point and within said first viewing plane π, asdefined by said angles α and Θ₃, to a third angle of inclination φ₃relative to said set of coordinates such that a projection or extensionof an image of said calibrated pointing device on said second imageplane passes through said further image of said target region, wherebysaid pointer points directly through said selected point toward saidtarget region, such that that respective images of pointing device areformed on said first and second image planes, along with imagescorresponding to said selected point and said target area; and needlemeans for casting an image on one at least one of said image planes,said needle means being pivotably mounted at a further pivot pointdifferent from said pivot point of said pointing device and beingconstrained for movement n plane defined by said pivot point, saidfurther pivot point and by said pointing device.
 14. A method fordetermining the required insertion depth for a biopsy needle so as tojust reach a selected target area within a body, wherein a properdirection for insertion of said biopsy needle has been priorlydetermined from a radiographic image on a viewing plane such that anextension of said direction of said biopsy needle from a selectedinsertion point into said body in a straight line leads through aselected target area, comprising the steps of: placing a biopsy needlesuch that an extension of said biopsy needle leads to a selected targetarea defining a plane containing said biopsy needle; placing a pointingneedle such that an extension of said pointing needle can lead throughsaid selected target area; placing a pointing needle, pivoted at one endand constrained to move within said plane; adjusting said pointingneedle, until a prolongation of the line of an image of said pointingneedle on said plane intersects said selected target area; andcalculating said required insertion depth from knowledge of a base linelength AC joining said pivot point and said selected insertion point andrespective angles, φ and φ₁, of said biopsy needle and said pointingneedle.
 15. A method for determining the required insertion depth for abiopsy needle in accordance with claim 14 including computing apparatusfor determining said required insertion depth by solving the equation${A\; C} = {{\sin\left( \phi_{1} \right)} \times {\frac{A\; B}{\sin\left( {\phi_{1} - \phi} \right)}.}}$16. Apparatus for determining the required insertion depth for a biopsyneedle priorly aligned for proper insertion into the body of a patientat a selected point on a surface of said body, so as to enter in astraight line passing through a designated target region within saidbody by the use of first and second image planes, such that at saidproper depth, an end of said needle just reaches said target area, saidapparatus comprising: a base portion including a circle portion having acenter point; a planar semicircular portion mounted onto said baseportion such that the diameter of said semicircular portion isconcentric with said center point and rotatable thereabout, saidsemicircle portion being further rotatable about a straight line throughsaid diameter; a straight pointing device having one end thereofpivotably affixed to said center point and being constrained formovement within a plane defined by said planar semicircular portion; andfirst and second substantially straight pointing needles, each havingone end thereof pivotably affixed at a respective end of said diameterof said semicircular portion and being constrained for movement within aplane defined by said planar semicircular portion.
 17. Apparatus fordetermining the required insertion depth for a biopsy needle inaccordance with claim 16, including means for measuring an angle θ ofsaid plane defined by said semicircular portion relative to said baseportion, an angle φ of said pointing device relative to said baseportion, and a respective angle φ₁, φ₂ defined by each of said pointingneedles relative to said base portion.
 18. Apparatus for determining therequired insertion depth for a biopsy needle in accordance with claim17, wherein at least one of said pointing needles is made of asubstantially radiation-transparent material.
 19. Apparatus fordetermining the required insertion depth for a biopsy needle inaccordance with claim 18, wherein said pointing needles are made of asubstantially radiation-transparent material and include imbeddedtherein markers that are relatively radiation-opaque as compared withsaid radiation-transparent material.
 20. Apparatus for determining therequired insertion depth for a biopsy needle in accordance with claim19, including computing apparatus for determining said depth by solvingthe equation${A\; C} = {{\sin\left( \phi_{1} \right)} \times {\frac{A\; B}{\sin\left( {\phi_{1} - \phi} \right)}.}}$21. Apparatus for positioning or aligning a biopsy needle for properinsertion into the body of a patient from a selected point on a surfaceof said body, so as to enter in a straight line passing through adesignated target region within said body, in conjunction with animaging system utilizing radiation from a first source position forderiving a first radiographic image on a first image plane of a portionof said body including a first image of said selected point and a firstimage of said target region, said first source position, said firstimage of said selected point, and said first image of said target regiondefining a first viewing plane π, said imaging system utilizingradiation from a second source position for deriving a secondradiographic image on a second image plane of said portion of said body,including a second image of said selected point and a second image ofsaid target region, said second source position, said second image ofsaid selected point, and said second image of said target region definea second viewing plane π′, said apparatus comprising: first measuringcircle means for establishing a first auxiliary plane at a first planeangle θ₁ with respect to a selected set of coordinates and forconstraining a pointer for moving rotatably about said selected pointand within said first auxiliary plane to a first angle of inclination θ₁relative to said set of coordinates such that a projection or extensionof an image of said pointer on said first image plane passes throughsaid first image of said target region; second measuring circle meansfor establishing a second auxiliary plane at a second plane angle θ₂with respect to said selected set of coordinates, said second planeangle being different from said first plane angle such that said firstand second auxiliary planes form an intersection line and forconstraining a pointer for moving rotatably about said selected pointand within said second auxiliary plane to a second angle of inclinationθ₂ relative to said set of coordinates such that a projection orextension of an image of said pointer on said first image plane passesthrough said first image of said target region, whereby said firstviewing plane π is uniquely defined by said angles θ₁, θ₂, φ₁, and φ₂relative to said set of coordinates; means for setting said pointer formoving rotatably about said selected point and within said first viewingplane π, now uniquely defined, to a third angle of inclination φ₃relative to said set of coordinates such that a projection or extensionof an image of said pointer on said second image plane passes throughsaid further image of said target region, whereby said pointer pointsdirectly through said selected point toward said target region.
 22. Amethod for positioning or aligning a biopsy needle for proper insertioninto the body of a patient from a selected point on a surface of saidbody, so as to enter in a straight line passing through a designatedtarget region within said body, said method comprising the steps of:utilizing radiation from a first source position for deriving a firstradiographic image on a first image plane of a portion of said bodyincluding a first image of said selected point and a first image of saidtarget region, said first source position, said first image of saidselected point, and said first image of said target region defining afirst viewing plane π; establishing a first auxiliary plane at a firstplane angle θ₁ with respect to a selected set of coordinates; moving apointer rotatably about said selected point and within said firstauxiliary plane to a first angle of inclination φ₁ relative to said setof coordinates such that a projection or extension of an image of saidpointer on said first image plane passes through said first image ofsaid target region; establishing a second auxiliary plane at a secondplane angle θ₂ with respect to said selected set of coordinates, saidsecond plane angle being different from said first plane angle such thatsaid first and second auxiliary planes form an intersection line; movingsaid pointer rotatably about said selected point and within said secondauxiliary plane to a second angle of inclination φ₂ relative to said setof coordinates such that a projection or extension of an image of saidpointer on said first image plane passes through said first image ofsaid target region, whereby said first viewing plane it is uniquelydefined by said angles θ₁, θ₂, φ₁, and φ₂ relative to said set ofcoordinates; utilizing radiation from a second source position forderiving a second radiographic image on a second image plane of saidportion of said body, including a second image of said selected pointand a second image of said target region, said second source position,said second image of said selected point, and said second image of saidtarget region define a second viewing plane π′; moving said pointerrotatably about said selected point and within said first viewing planeπ, now uniquely defined, to a third angle of inclination φ₃ relative tosaid set of coordinates such that a projection or extension of an imageof said pointer on said second image plane passes through said furtherimage of said target region, whereby said pointer points directlythrough said selected point toward said target region.
 23. A method forpositioning a guide for a biopsy needle for its proper insertion intosaid body of a patient from a selected point on a surface of said body,so as to enter in a straight line passing through a designated targetregion within said body, in conjunction with an imaging system utilizingradiation from first and second source positions for deriving first andsecond radiographic images, said method including: (a) selecting a firstauxiliary plane at an angle θ₁; moving said guide within said firstauxiliary plane to an angle φ₁ so as to cause said guide image on saidfirst image plane to be aligned in a straight line through said targetregion; (b) storing said angle φ₁; (c) selecting a second, different,auxiliary plane at an angle θ₁; (d) moving said guide to an angle φ₂within said second auxiliary plane so as to cause said guide image onsaid second image plane to be aligned in a straight line through saidtarget region; (e) storing values for said angles θ₂ and φ₂; (f)calculating, by utilizing values stored for said angles, rotations α andθ so as to derive a first viewing plane π; and (g) moving said guidewithin said first viewing plane π to an angle φ₃ so as to cause saidguide image on said second image plane to be aligned in a straight linethrough said target region, whereby said guide is properly aligned. 24.A method for positioning a guide for a biopsy needle in accordance withclaim 23, wherein α and θ are defined by[θ=arc sin(∥L ₁wedgeL ₂∥)] and$\alpha = {\arccos\left( \frac{{{L_{1}\lbrack 3\rbrack}{L_{2}\lbrack 1\rbrack}} - {{L_{1}\lbrack 1\rbrack}{L_{2}\lbrack 3\rbrack}}}{\sqrt{\left( {{{L_{1}\lbrack 3\rbrack}{L_{2}\lbrack 1\rbrack}} - {{L_{1}\lbrack 1\rbrack}{L_{2}\lbrack 3\rbrack}}} \right)^{2} + \left( {{{L_{1}\lbrack 3\rbrack}{L_{2}\lbrack 2\rbrack}} - {{L_{1}\lbrack 2\rbrack}{L_{2}\lbrack 3\rbrack}}} \right)^{2}}} \right)}$where Λ is the vector product defined in ³2, 3-dimensional space. 25.Apparatus for positioning or aligning a biopsy needle for properinsertion into the body of a patient from a selected point on a surfaceof said body, so as to enter in a straight line passing through adesignated target region within said body, in conjunction with animaging system utilizing radiation from a first source position forderiving a first radiographic image on a first image plane of a portionof said body including a first image of said selected point and a firstimage of said target region, said first source position, said firstimage of said selected point, and said first image of said target regiondefining a first viewing plane π, said imaging system utilizingradiation from a second source position for deriving a secondradiographic image on a second image plane of said portion of said body,including a second image of said selected point and a second image ofsaid target region, said second source position, said second image ofsaid selected point, and said second image of said target region definea second viewing plane π′, said apparatus comprising: measuring circlemeans having a first position for establishing a first auxiliary planeat a first plane angle θ₁ with respect to a selected set of coordinatesand for constraining a pointer for moving rotatably about said selectedpoint and within said first auxiliary plane to a first angle ofinclination φ₁ relative to said set of coordinates such that aprojection or extension of said image of said pointer on said firstimage plane passes through said first image of said target region; saidmeasuring circle means having a second position for establishing asecond auxiliary plane at a second plane angle θ₂ with respect to saidselected set of coordinates, said second plane angle being differentfrom said first plane angle such that said first and second auxiliaryplanes form an intersection line and for constraining a pointer formoving rotatably about said selected pint and within said secondauxiliary plane to a second angle of inclination φ₂ relative to said setof coordinates such that a projection or extension of an image of saidpointer on said first image plane passes through said first image ofsaid target region, whereby said first viewing plane it is uniquelydefined by said angles θ₁, θ₂, φ₁, and φ₂ relative to said set ofcoordinates; means for setting said pointer for moving rotatably aboutsaid selected point and within said first viewing plane π, now uniquelydefined, to a third angle of inclination φ₃ relative to said set ofcoordinates such that a projection or extension of an image of saidpointer on said second image plane passes through said further image ofsaid target region, whereby said pointer points directly through saidselected point toward said target region.